English

Unitary forms for holomorphic vertex operator algebras of central charge $24$

Quantum Algebra 2023-03-22 v1

Abstract

We prove that all holomorphic vertex operator algebras of central charge 2424 with non-trivial weight one subspaces are unitary. The main method is to use the orbifold construction of a holomorphic VOA VV of central charge 2424 directly from a Niemeier lattice VOA VNV_N. We show that it is possible to extend the unitary form for the lattice VOA VNV_N to the holomorphic VOA VV by using the orbifold construction and some information of the automorphism group Aut(V)\mathrm{Aut}(V).

Keywords

Cite

@article{arxiv.2211.15952,
  title  = {Unitary forms for holomorphic vertex operator algebras of central charge $24$},
  author = {Ching Hung Lam},
  journal= {arXiv preprint arXiv:2211.15952},
  year   = {2023}
}